Stats

1 Equity999.26,3%29.9778,25%249.815,cap280.2 Retain prior gap assumptions g EEM.125794155019/QQQ.109666233203/IWM.138906519177, not smaller current sample maxima. r=2ATR/E;k=r+(1-r)*2g+.005;N=floorcents min(280/3,.25equity,(.03equity-.50)/k).3 Sizes93.33 each. Stop-plus-gap stress incl.50fixedreserve EEM26.413233,QQQ23.108078,IWM28.421384; joint77.942695 (7.8000%equity approximate). Normalstop dollar losses2.62669/2.14064/2.11364.4 Numpy20000IID paths of20 synchronized raw-gap draws from1254rows,seed92104:Q95worst daily basketloss10.014485,Q99/max14.835991,excludescosts/stops/drift. Conclusion unchanged sizes within assumed per-lot stress; neither model guarantees futureloss<3%. Counterexample unseen correlated crash/session outage exceeds sample and scenario; total loss of93.33lot exceeds3%. No calibrated live win probability/Kelly from empty ledger; fixed equal mandate sizing governs. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip .

Premises: equity999.38,3% ceiling29.9814,positioncap249.845,fund280. Retain prior gap assumptions EEMg=.125794155019,QQQ=.109666233203,IWM=.138906519177. r=2ATR/E; N=floorcents min(280/3,.25equity,(.03equity-.50)/(r+(1-r)*2g+.005)). All N93.33. Stress EEM26.413233,QQQ23.108078,IWM28.421384 incl .50/lot; joint77.942695. These scenarios are not guaranteed maximum losses. Reference brackets and payoff:[{"symbol":"QQQ","size":93.33,"stop":704.90264,"target":838.105554290121,"p90_pct":16.169596547248037,"rr":7.049798535241943,"normal_loss":2.1406405278259037,"stress":23.108077650841185,"fall_to_sma_pct":8.271862221914205},{"symbol":"IWM","size":93.33,"stop":277.666,"target":320.542353437563,"p90_pct":12.827297936488211,"rr":5.6640275781105,"normal_loss":2.1136403379091897,"stress":28.421384363225883,"fall_to_sma_pct":3.7273319253783965},{"symbol":"EEM","size":93.33,"stop":65.1435,"target":74.21621874551062,"p90_pct":10.720899217530388,"rr":3.809286374508678,"normal_loss":2.626690213337311,"stress":26.413232637416957,"fall_to_sma_pct":7.367522005072347}]. Numpy seed92102:20000 paths*20 days, synchronized IID resampling1254 overnight gap vectors; Q95 largest single-night basket loss10.023785,Q9914.828643. No stops/drift/serial dependence modeled, excludes unseen gaps; not live exit odds or strategy backtest and not used to shrink stress. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all

Scenario analysis, not new Monte Carlo or calibrated exit odds. Retain prior3690 adverse-gap inputs EEM .125794155019,QQQ .109666233203,IWM .138906519177, not newly estimated tails. Let r=2ATR/E,g=retained gap,N=floorcents min(280/3,250,(30-.50)/(r+(1-r)*2g+.005)). Stress=N*(r+(1-r)*2g+.005)+.50. Updated reference entries produce [{"symbol":"QQQ","size":93.33,"stop":704.90264,"target":838.105554290121,"p90_pct":16.169596547248037,"rr":7.049798535241943,"sma_cushion_pct":9.017802412958599,"fall_to_sma_pct":8.271862221914205,"stress":23.108077650841185,"gap_beyond_stop_for_30":0.2949106082972351,"normal_stop_loss":2.1406405278259037},{"symbol":"IWM","size":93.33,"stop":277.666,"target":320.542353437563,"p90_pct":12.827297936488211,"rr":5.6640275781105,"sma_cushion_pct":3.8716408300737193,"fall_to_sma_pct":3.7273319253783965,"stress":28.421384363225883,"gap_beyond_stop_for_30":0.2951193158969985,"normal_stop_loss":2.1136403379091897},{"symbol":"EEM","size":93.33,"stop":65.1435,"target":74.21621874551062,"p90_pct":10.720899217530388,"rr":3.809286374508678,"sma_cushion_pct":7.953497698156986,"fall_to_sma_pct":7.367522005072347,"stress":26.413232637416957,"gap_beyond_stop_for_30":0.29113226241437123,"normal_stop_loss":2.626690213337311}]. Joint77.942695 includes1.50 reserve; no independent-loss assumption. Reverse stress solves gap beyond stop causing30 loss: approximately29.11–29.51%. Larger gaps can breach3%; complete lot loss93.33 exceeds it. Stress envelope is sizing assumption, not guaranteed bound. Prior Monte Carlo3646 retained without repeating it; no backtest or odds invented. Source https://runway.adityaperswal.workers.dev/data/stock-bars plus saved3690.

Premises:1 common-date adjusted gaps training2021–2024 N1004;2 synchronized5-session blocks preserve cross-asset shocks and short serial dependence;3 20000 paths20sessions, seed92006;4 fixed93.33 notionals each. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all . Simulated maximum single-night basket loss Q50/95/99=3.913011/7.974398/14.828643USD; zero sampled paths exceed30. This zero is bounded empirical support, NOT zero real tail risk, a portfolio loss limit or live exit probability. Excludes intraday paths, trading costs, stop-through gaps, changing notionals and unseen shocks; no Kelly inferred. EEM holdout threshold exceeds nominal1% frequency (3644), directly challenging stationary extrapolation. Retain separately the stop-through-gap scenario r=2ATR/E,c=r+(1-r)*2g+.005,g=.125794155019/.109666233203/.138906519177; size=floorcents min(280/3,250,29.5/c). Results [{"symbol":"EEM","size":93.33,"stop":65.1435,"target":74.21425092953517,"p90":0.10717963493264468,"rr":3.8082432703605487,"stress":25.913232637416957},{"symbol":"QQQ","size":93.33,"stop":704.90264,"target":838.105473380901,"p90":0.1616958533244174,"rr":7.049793645687354,"stress":22.608077650841185},{"symbol":"IWM","size":93.33,"stop":277.666,"target":320.5246054777956,"p90":0.12821050854556687,"rr":5.661269113738809,"stress":27.921384363225883}]. Joint76.442695USD; modeled per-lot<30 but shocks outside assumptions can exceed3% equity. No increase in size from benign bootstrap quantiles.

Premises:1 current reference entries/ATR from3607;2 carried gap assumptions g EEM.125794155019 QQQ.109666233203 IWM.138906519177, not fresh tail estimates;3 cash1000/fund280/position250. r=2ATR/E; coefficient=r+(1-r)*2g+.005; size=floorcents min(280/3,250,29.5/coefficient). Gives93.33each. Stress EEM25.913233 QQQ22.608078 IWM27.921384 joint76.442695USD, each<30 under modeled shocks. Larger shocks can exceed3%; no guaranteed bound or calibrated odds. Source https://runway.adityaperswal.workers.dev/data/stock-bars . Prior unchanged-sample Monte Carlo3570 retained, not rerun as new evidence. Actual payout/stop slippage and distribution timing unknown. No trade-derived Kelly from empty reset ledger; equal-weight mandate governs.

Premises:1 initial93.33each;2 r=2ATR/entry;3 retained g assumptions EEM.125794155019 QQQ.109666233203 IWM.138906519177 from prior fund stress, not new guaranteed bounds. Size=floorcents min(280/3,250,29.5/(r+(1-r)*2g+.005)) gives93.33each. Stress=N*(r+(1-r)*2g+.005): EEM25.913233,QQQ22.608078,IWM27.921384, joint76.442695. Each modeled loss<30 account3%; larger gaps can exceed this. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all. Separate seed92002 jointIID20000x20day closing-return paths last1260 observations: P05 -22.652306,median2.100807,P9528.781054 dollars. Repeated unchanged-sample diagnostic is NOT new evidence. No costs/stops/targets/intraday sequence/serial dependence; current basket retrospectively selected. Neither live exit odds nor Kelly estimate; no sizing change.

Premises:1 same-day joint rows of last1260returns preserve cross-asset dependence;2 numpy seed920,20000paths of20 IID sessions;3 constant initial93.33 each and compounded closes. P05 -22.5286USD,median2.0020,P9528.8353. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all. This repeat is a reproducibility diagnostic of new retrieval, not fresh independent evidence; prior3463 already established dependence. No stops/targets/intraday exits/costs/serial dependence; 2020crisis omitted, retrospectively selected basket, no calibrated trade odds or Kelly input. Separate retained scenario r=2ATR/entry; stress=N*(r+(1-r)*2g+.005), g EEM.125794155019 QQQ.109666233203 IWM.138906519177 from prior record, not remeasured extrema. EEM25.9132 QQQ22.6081 IWM27.9214,joint76.4427USD. Size=floorcents min(280/3,250,29.5/(r+(1-r)*2g+.005)) yields93.33 each. Every lot below30 in this stated scenario, but complete loss93.33 could exceed3% account; empirical envelopes cannot guarantee maximum overnight loss. No inferred safe bound or size uplift.

Premises:1 1255 synchronized daily returns Sep20 2021–Sep18 2026;2 fixed today's EEM/QQQ/IWM93.33 initial dollars each, buy-and-hold compounding20sessions;3 numpy20000paths seed91906;4 compare joint IID rows with independent perasset IID rows, then joint5sessionblocks for serial sensitivity. Same-day dependence isolation: P05 PnL -22.4160 versus -13.4391 USD, ES05 -28.6110 versus -17.1955; model probability loss>30 1.505% versus .015%. Joint5dayblock P05 -21.6557,ES05 -28.4310,P01 -32.7992,lossfrequency42.17%,loss>30 1.58%. Full results {"N":20000,"H":20,"block":5,"sample":1255,"start":"2021-09-20","end":"2026-09-18","seed":91906,"joint_block":{"p01":-32.79919741904743,"p05":-21.655714707388654,"median":2.909658317689602,"mean":2.714465051489629,"prob_loss":0.4217,"prob_loss30":0.0158,"es05":-28.431048746217193},"joint_iid":{"p01":-32.76254907968935,"p05":-22.41602014010171,"median":1.9648147526769801,"mean":2.5320445311655244,"prob_loss":0.44905,"prob_loss30":0.01505,"es05":-28.61101950104886},"independent_iid":{"p01":-19.57023865210427,"p05":-13.439106213579274,"median":2.5778309022182273,"mean":2.6777364221379094,"prob_loss":0.39825,"prob_loss30":0.00015,"es05":-17.1955094610215},"correlation":{"EEM":{"EEM":1,"QQQ":0.6929633476476149,"IWM":0.6507916837227055},"QQQ":{"EEM":0.6929633476476149,"QQQ":1,"IWM":0.7785802945417117},"IWM":{"EEM":0.6507916837227055,"QQQ":0.7785802945417117,"IWM":1}}}. Validity: dependence alters basket distribution; soundness limited to empirical stationary return model. Today's basket retrospectivelyselected, 2020excluded, no execution/stops/targets/ratchets/costs, no held-out strategy or actual winrate. These probabilities are conditional model frequencies, NOT calibrated forecasts, exit odds or Kelly inputs. No size uplift or momentum veto. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all

Premises:1 synchronized gap series and today's93.33 weights from3426;2 resample common basket rows preserving crossasset dependence;3 numpy10000draws seed91904. IID within calendar groups mean weekend-minus-ordinary-.147572USD, CI95[-.486861,.179403];20day moving blocks preserving chronological labels CI[-.473665,.229915]. Both crosszero: no robust average weekend penalty established. Blocks do not establish stationarity or future tails. This is estimation simulation, NOT a momentumbacktest/target-hit model/stop-execution simulation; no winrate or Kelly odds inferred. Frozen earlier longer-history envelopes EEM.125794155019/QQQ.109666233203/IWM.138906519177 remain stress assumptions, not current5year maxima. Do not replace them with smaller latest5year observed tails, which omit2020. Current stop-plus-double-envelope-plus50bp scenario remains25.913233/22.608078/27.921384USD perlot,76.442695joint, not guaranteed bound. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all .

Premises:1 planned93.33each;2 last756 common completed daily returns;3 numpy seed91902 resamples10000 paired contiguous5day blocks preserving crossasset dependence. Terminal dollarP01 -15.174916/P05 -9.811266/median1.411593/worstsample -34.060647;39.95%negative. Not stop/target execution model, independent observations or live exit odds; no fees/halting/new gap support. Updated because capital and weights changed. Current basket selected with hindsight; no trading backtest or fresh validation. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all . Larger novel gaps can exceed model and perlot scenario.

Premises:1 selected current notionals90.04/103.20/83.56;2 last756 completed common daily returns endingSep18;3 numpy seed919 samples10000 paired contiguous5day blocks preserving observed cross-asset dependence. Dollar five-day terminal distribution P01=-13.839929,P05=-9.600495,median=1.469630,worst sampled=-33.635197;39.46% negative. Static buy-and-hold risk diagnostic, no stop fills/target enforcement/fees, no independent holdout strategy validation. Overlapping repeated paths do not create10000 independent observations. Daily-path bootstrap misses novel gaps, halts, weekend jumps beyond history and intraday stops; NOT live loss odds, target-hit probability or Kelly inputs. Consequence: retain stronger frozen double-gap stress for size, do not increase deployment because bootstrap tails look small. No repeated strategy backtest because fixed mandate explicitly forbids it. Source https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=all .

Premises:1 statistical risk audit uses428daily return vectors2025-01-02–Sep17 2026 for current89.95/103.11/83.46 notionals;2 resample vectors jointly to preserve contemporaneous cross-asset dependence;3 circular blocks5sessions retain short clusters, 10000replicates, seed9180601. Per replicate sample428days, calculate empirical95% expected-shortfall tail mean,99%loss quantile and mean of frozen threshold-exceedance indicators. Results originalES95=7.609460USD, percentile95% bootstrap interval[5.947080,9.492035]; VaR99=9.368118 interval[6.596389,13.503072]; threshold coverage exceedance.934579% interval[0,2.102804]%. These are Monte Carlo uncertainty intervals for historical daily mark-risk estimates, NOT prospective loss limits, exit odds, independent OOS strategy returns or a Kelly estimate. Resampling observations already inspected and choosing current symbols retrospectively means no new edge evidence. Blocks cannot create novel shocks; 428days and ~22tail observations leave material uncertainty. Circular joins approximate, block length unoptimized; no claim calibrated CI coverage. No repeat static stop/target bootstrap. Decision preserve mandate and earlier crisis stress, do not enlarge sizes because threshold count resembles1%. Costs and actual RTH stop execution absent from return sample; 50bp only in separate stress. Counterexample prolonged halt/new gap is outside bootstrap support. Source https://runway.adityaperswal.workers.dev/data/stock-bars ; quant.py/quant_results.json.

Premises:1 joint09:45return vectors from41crisis and29recent sessions preserve crossasset dependence;2 independently resample20000 paths of60nights, seed20260913;3 old equal lots and hypothetical initialstop preceding shock plus50bp, maximum-night loss not compounded portfolio PnL. Crisis median/P95/max all40.66658; recent all9.58880. Small conditioned samples repeatedly include their worst day, so the percentile has no forward tail-probability interpretation. Regime frequency, clustering, ratchet, executable fills and novel losses omitted. Conclusion retain explicit doubled-crisis envelope for sizing, do not use this bootstrap to estimate win odds, expected return or halfKelly. This is scenario simulation, not a strategy backtest. Source https://runway.adityaperswal.workers.dev/data/stock-bars.

Premises:1 fiveyear1255 joint dailygap vectors preserve crossasset dependence;2 iid20000paths60nights seed20260913;3 hypothetical initialstop before adverse overnightgap, plus50bp. {"paths":20000,"nights":60,"sample":1255,"p50":13.102510465679082,"p95":16.966882644386843,"max":20.658827830036604}. Reproduces3002; maximum-night loss distribution, not compounded portfolio PnL or target odds. Omits2020, regime clustering, ratchet and novel gaps; stricter crisis stress controls sizing. No win-rate/Kelly estimate inferred. Source https://runway.adityaperswal.workers.dev/data/stock-bars.

Premises:1 fixed prospective sizes and initial2ATR distances;2 joint all-adjusted open/previousclose vectors since2021-09-13 preserve same-night asset dependence;3 iid sample20000paths of60nights seed20260913;4 each night hypothetical stop reached before adverse gap, loss=N*[r+(1-r)*max(-gap,0)+.005]. Distribution of maximum joint nightly loss: {"paths":20000,"nights":60,"historical_nights":1255,"joint_max_loss_p50":13.102510465679082,"joint_max_loss_p95":16.966882644386843,"joint_max_loss_max":20.658827830036604,"single_lot_max":7.657745018977896,"seed":20260913}. Descriptive stress, not compounded strategy PnL, independent validation, live win odds or Kelly. Excludes2020; does not model dynamic ratchet, clustered regimes or novel tails; crisis-inclusive doubledgap statistical analysis is the stricter sizing scenario. Source https://runway.adityaperswal.workers.dev/data/stock-bars . Prior frozen-barrier simulation2905 retained separately; no mandate re-test.

Premises:1 actual completed split-adjusted OHLC daily vectors Sept13 2021–Sep11 2026 N1255;2 current initial stop fractions2.2013275/2.1257399/1.6511153% and P90 targets16.1695853/12.8238446/9.6302829%;3 resample synchronized five-session blocks jointly across3assets,20000paths of60sessions,seed2026091206;4 normalize each O/H/L/C to priorC and compound synthetic prices, first barrier touched exits, opening gaps fill at open, intraday barriers at threshold;5 assumed6bp per side costs, no reinvestment. Compare stop-first and target-first when daily both touch:0 ambiguous paths and identical output. QQQ stop77.655%,target12.780%,timeout9.565%,meanexit18.30565sessions,meannet+.876683%,P05-2.976048%;IWM81.095/14.325/4.580%,14.8415sessions,+.185055%,P05-2.871990%;EFA76.485/16.685/6.830%,17.71015sessions,+.342275%,P05-3.046753%. At62.40/62.41/62.41 dollars bookmean+.876157,median-3.953189,P05-5.082488,P95+21.317089, sampled3%accountbreaches0. Output shows a low hit rate can coexist with a fat right tail, not a verified tradable expectancy. Crucial exclusions: no profit-triggered SMA/ATR ratchet, monthly rank changes, 15min check delay, bids/asks, future dividends/cash, or novel tail shocks; fiveyear history omits2020. Daily threshold fills may be optimistic versus actual monitoring. Blocks preserve short serial and same-day crossasset structure but not long regime persistence. Results are model-dependent first-passage diagnostics, NOT OOS strategy performance, calibrated real win odds, Kelly inputs, or a guarantee. Mandate unchanged; do not gate deployment or change targets on this output. Sources https://runway.adityaperswal.workers.dev/data/stock-bars?feed=sip&adjustment=split ; live signal2903 and gap stress preceding statistical analysis.

Premises:1 account850.99/fund144.67;2 fixed notionals48.22/48.22/48.23;3 stop distances2.2013275/2.1257399/1.6511153%;4 adverse gap applied multiplicatively beyond stop;5 50bp extra liquidation friction is an assumption, not measured spread. Loss_i=N_i*[r_i+(1-r_i)*g_i+.005]. Ordinary total stop loss$2.882845. Five-year double-worst loss$6.35524/$6.24496/$5.30789 per lot. Crisis-inclusive double-worst loss$10.22234/$10.04622/$12.06440, each1.18–1.42% equity<3%, but joint sum$32.33296=3.79945% equity. Simultaneous20% beyond stops+50bp loses$31.963626=3.75605%;10% loses$17.784910=2.08991%. Thus per-position compliance in these stress scenarios does NOT imply book-level3% limit. All-three total loss would be17.0002% equity; one total-loss lot5.666–5.668%. Guaranteeing a per-lot3% loss bound requires each notional below$25.5297 (e.g.$25.52); guaranteeing it for whole book requires total below$25.5297. Those are hard arithmetic bounds, not the recommended equal-slot stress interpretation. Monte Carlo numpy RNGseed20260912:50,000 paths of60 independently sampled historical joint gap vectors, preserving contemporaneous cross-ETF dependence, fixed notionals/current stop distances, record maximum single-night adverse stress loss per path. Five-year N1255 P95$8.481268,P99$10.328320; expanded2016–26 N2687 P95$13.431428,P99$17.969580. Zero sampled paths exceed$25.5297 because bootstrap cannot generate unseen worse gaps; zero is NOT estimated impossibility. Model has no price drift, serial clustering, compounding, dynamic stop lifecycle, historical entries, targets, liquidation quotes or win probabilities. It is neither strategy backtest nor profit forecast. Daily tail dates checked against opening15min: Aug5 2024 IWM gap-5.27475% vs09:45 proxy-5.49971%; Mar3 2026 EFA-4.50145% vs09:45-4.79187%. Six symbol/date checks show delay can worsen or improve fills; IWM daily vs15min first open197.90/197.95 also differ. 50bp is not a guaranteed delay allowance. Sources https://runway.adityaperswal.workers.dev/data/stock-bars?timeframe=1Day&feed=sip&adjustment=split and same endpoint timeframe=15Min. Adopt scenario-based sizing evidence, reject guaranteed-loss and calibrated-exit-odds claims.